分形测度棱镜下的强测度零集和弱可加集
Strong measure zero and meager-additive sets through the prism of fractal measures
摘要：
我们发展了一个与Borel的\emph{strong measure zero}相似的\emph{sharp measure zero}集理论，并证明了一个类似于Galvin-Myscielski-Solovay定理的定理，即一个实数集有锐测度零当且仅当它是弱可加的.一些后果：$2^ω$的子集是弱可加的当且仅当它是$\mathcal E$ -可加的;如果$f:2^ω\to2^ω$是连续的并且$X$是弱可加的，那么$f(X)$也是。
英文摘要：
We develop a theory of \emph{sharp measure zero} sets that parallels Borel's \emph{strong measure zero}, and prove a theorem analogous to Galvin-Myscielski-Solovay Theorem, namely that a set of reals has sharp measure zero if and only if it is meager-additive. Some consequences: A subset of $2^ω$ is meager-additive if and only if it is $\mathcal E$-additive; if $f:2^ω\to2^ω$ is continuous and $X$ is meager-additive, then so is $f(X)$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
